Determine acceleration of a 2D shape when pushed from any point in its area

[eegg]

I'm designing a user interface for the web, and it has a physics component. I'm no physicist, but I've got some way towards specifying the problem. Hopefully, someone can help me fully understand it.

Here's the scenario. A piece of paper is on the table at a specific location and rotation. You place your finger on any point on the paper's surface, then move your finger across the table to a second point. The paper moves with your finger, coming to rest at a new location and rotation.

The problem: given the starting location and rotation, plus the start and end points of your finger, how do we completely determine the movement of the paper? (Is the problem completely specified so that there is an answer?)

My intention is that this scenario, simulated on screen, will be the basis of a naturalistic user interface in which one can translate *and* rotate 2D objects using *only* click-and-drag. I've made prototypes which are not physically accurate, but I'm not satisfied.

I've partially thought it through; I think that:

* The state of the shape can be specified as velocity and angular velocity around a point, with a simulation of friction bringing it to a stop.
* The acceleration imparted by the finger must be broken into two components: toward the center of mass, and perpendicular to it.

I don't think this is the full story though. I need to ensure that the shape is always "pinned" at the finger. E.g., I move the paper across the table, then stop but keep my finger there: all velocity the paper has is converted to rotation about the finger.

A further problem is that I don't understand how acceleration/velocity is converted to angular velocity under this constraint.

Can someone help me out or point in the right direction?

 

[eljose79]

Hello,

As a scientist with a background in physics, I can help you with your problem. It seems like you have a good understanding of the basic principles involved, but there are a few key concepts that will help you fully understand the movement of the paper.

Firstly, you are correct in thinking that the state of the paper can be described by its velocity and angular velocity. However, there are a few other factors that come into play. One is the moment of inertia, which is a measure of how difficult it is to rotate an object around a specific axis. This will depend on the shape and mass distribution of the paper.

Secondly, the force applied by your finger will not only have a component towards the center of mass, but also a torque component. This torque will cause the paper to rotate around its center of mass.

To ensure that the paper is always "pinned" at the finger, you will need to apply a force and torque that counteract the paper's movement and rotation. This can be achieved by using a virtual pivot point at the location of the finger, and calculating the appropriate forces and torques to keep the paper in place.

As for converting acceleration/velocity to angular velocity, there are equations that relate these quantities, taking into account the moment of inertia. However, in order to fully determine the movement of the paper, you will also need to consider the friction between the paper and the table, which will affect its velocity and angular velocity.

I suggest consulting with a physics textbook or seeking assistance from a physics expert to fully understand and implement the physics component of your user interface. Good luck with your project!